Answer:
[tex]a=15[/tex]
[tex]b=\frac{1}{3}[/tex]
Step-by-step explanation:
we have an exponential function of the form
[tex]y=a(b^x)[/tex]
where
a is the initial value or y-intercept
b is the base
Looking at the graph
we can see the ordered pairs (0,15) and (1,5)
(0,15) ---> y-intercept
so
The value of a is equal to
[tex]a=15[/tex]
substitute
[tex]y=15(b^x)[/tex]
with the point (1,5) find the value of b
For x=1, y=5
substitute in the exponential function
[tex]5=15(b^1)[/tex]
solve for b
[tex]5=15(b)[/tex]
[tex]b=\frac{1}{3}[/tex]
therefore
The exponential function is
[tex]y=15(\frac{1}{3}^x)[/tex]
